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# If x > 1, what is the value of x?

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Manager
Joined: 22 Mar 2011
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If x > 1, what is the value of x? [#permalink]

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02 Jun 2011, 18:35
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Question Stats:

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If x > 1, what is the value of x?

(1) There are x unique factors of x.
(2) The sum of x and any prime number larger than x is odd.

[Reveal] Spoiler:
i) is understood

ii) The sum of x and any prime number larger than x is odd.

i.e if x > 1 then x has to be atleast 2 (the only prime number that is also even)

E + or - O = ODD

So only 2 will fulfill this criteria. If we take any prime number greater than 2 then O + or - O = Even.

So the answer should be each statement alone is sufficient.

Please clarify.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-1-what-is-the-value-of-integer-x-110661.html
[Reveal] Spoiler: OA

Kudos [?]: 16 [0], given: 10

Math Forum Moderator
Joined: 20 Dec 2010
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Re: If x > 1, what is the value of x? [#permalink]

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02 Jun 2011, 19:03
melguy wrote:
If x > 1, what is the value of x?

i) There are x unique factors of x.
ii) The sum of x and any prime number larger than x is odd.

i) is understood

ii) The sum of x and any prime number larger than x is odd.

i.e if x > 1 then x has to be atleast 2 (the only prime number that is also even)

E + or - O = ODD

So only 2 will fulfill this criteria. If we take any prime number greater than 2 then O + or - O = Even.

So the answer should be each statement alone is sufficient.

Please clarify.

St2:
x is not necessarily prime.
x is definitely even.
4+7=11(odd); x=4, Prime Number greater than x(4) is 7; 7+4=odd
6+7=13(odd); x=6, Prime Number greater than x(6) is 7; 6+7=odd
Not Sufficient.
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Manager
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Posts: 65

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Re: If x > 1, what is the value of x? [#permalink]

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02 Jun 2011, 19:06
St2:
x is not necessarily prime.
x is definitely even.
4+7=11(odd); x=4, Prime Number greater than x(4) is 7; 7+4=odd
6+7=13(odd); x=6, Prime Number greater than x(6) is 7; 6+7=odd
Not Sufficient.[/quote]

duh! Thanks for pointing out the mistake! I am just too tired and burnt out exam in 24 days

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Senior Manager
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Re: If x > 1, what is the value of x? [#permalink]

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02 Jun 2011, 20:42
So as per statement, is x=2?

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Re: If x > 1, what is the value of x? [#permalink]

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03 Jun 2011, 01:59
agdimple333 wrote:
So as per statement, is x=2?

Yes, as the statement1.
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Director
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Re: If x > 1, what is the value of x? [#permalink]

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03 Jun 2011, 17:47
1. Sufficient

as 2 is >1 and has 2 unique factors 1 and 2.

every other x >1 does not have x unique factors.

2. Not sufficient

x + prime greater than 1 is odd

as x >1

x ( x + odd = odd => x must be even)
2 + 3 is odd
4 + 5 is odd

Answer is A.

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Re: If x > 1, what is the value of x? [#permalink]

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19 Jun 2016, 02:40
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Re: If x > 1, what is the value of x? [#permalink]

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19 Jun 2016, 09:47
If x>1, what is the value of integer x?

(1) There are x unique factors of x --> x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x, inclusive but x can not be divisible by x-1 unless x=2, for example 3 is not divisible by 2, 4 is not divisible by 3, etc, but 2 is divisible by 1 (other value of x which has x distinct positive factors (1) is excluded by the stem as x>1). So this statement implies that x=2. Sufficient.

(2) The sum of x and any prime number larger than x is odd --> x+prime=odd, now as x itself is more than 1 then prime more than x cannot be 2 thus it's odd and we have x+odd prime=odd --> x=even, so x could be ANY even number. Not sufficient.

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-1-what-is-the-value-of-integer-x-110661.html
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Re: If x > 1, what is the value of x?   [#permalink] 19 Jun 2016, 09:47
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# If x > 1, what is the value of x?

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